Fats or oils containing a high concentration of diglycerides are widely used as edible oils because they have pharmacological actions such as a body fat burning action. Diglyceride-rich fats or oils prepared in the conventional manner contain impurities such as fatty acids, monoglycerides and odor components, so that when the diglyceride-rich fats or oils are used as an edible oil, a step of removing these impurities therefrom is necessary for improving its taste. It is common practice to carry out the so-called deodorizing operation, that is, the operation of bringing a fat or oil into contact with steam under conditions of a high temperature and reduced pressure (JP-B-1991-7240).